A cylinder has two circular ends, each with an area of 1256 c,. The height if the cylinder us 60 cm. what is the surface are of the cylinder?
plz explain the formula and all the steps towards how u got the answer... thank u!!!
To find the surface area of a cylinder, you need to calculate the areas of the two circular ends and the curved surface area.
1. Find the area of one circular end:
The formula for the area of a circle is A = πr², where A is the area and r is the radius.
Given that the area of each circular end is 1256 cm², we can rearrange the formula to solve for the radius:
1256 = πr²
Divide both sides of the equation by π:
1256/π = r²
Take the square root of both sides to find the radius:
√(1256/π) = r
2. Calculate the radius using a calculator:
√(1256/π) ≈ 20 cm (rounded to two decimal places)
3. Now that you have the radius, you can find the curved surface area (side area) of the cylinder:
The formula for the curved surface area of a cylinder is CSA = 2πrh, where CSA is the curved surface area, r is the radius, and h is the height.
Plug in the values:
CSA = 2π × 20 cm × 60 cm
CSA ≈ 7539.82 cm² (rounded to two decimal places)
4. Finally, calculate the total surface area of the cylinder:
The total surface area of a cylinder is the sum of the areas of the two circular ends and the curved surface area.
TSA = 2A_circular_end + CSA
TSA = 2 × 1256 cm² + 7539.82 cm²
TSA ≈ 10052.82 cm² (rounded to two decimal places)
Therefore, the surface area of the cylinder is approximately 10052.82 cm².
To find the surface area of a cylinder, we need to consider the areas of the two circular ends and the curved surface area (or lateral surface area) of the cylinder.
Let's start by finding the radius of the circular ends. The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius.
Given that the area of each circular end is 1256 cm^2, we can rearrange the formula to solve for the radius:
1256 = πr^2
First, divide both sides of the equation by π:
1256/π = r^2
Next, take the square root of both sides to find r:
√(1256/π) = r
Now that we know the radius, we can calculate the curved surface area. The formula for the curved surface area of a cylinder is A = 2πrh, where A is the area, π is a mathematical constant (approximately 3.14159), r is the radius, and h is the height.
Substituting the values we have:
A = 2πrh = 2π(√(1256/π))(60)
Simplifying further:
A = 2π(60√(1256/π))
= 2π(60)(√(1256/π))
= 120π(√(1256/π))
Finally, we can calculate the surface area by adding the areas of the two circular ends to the curved surface area:
Surface Area = 2(1256) + 120π(√(1256/π))
Surface Area = 2512 + 120π(√(1256/π))
And that's how we calculate the surface area of the cylinder using the given formula and all the necessary steps.